Question: What do the following two equations represent? $3x+2y = 1$ $-6x+9y = 5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $3x+2y = 1$ $2y = -3x+1$ $y = -\dfrac{3}{2}x + \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $-6x+9y = 5$ $9y = 6x+5$ $y = \dfrac{2}{3}x + \dfrac{5}{9}$ The slopes are negative inverses of each other, so the lines are perpendicular.